Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making

Zeeshan Ali,Gustavo Santos-García,Tahir Mahmood

doi:10.3390/math9212730

Zeeshan Ali, Gustavo Santos-García + Show 1 more

Open Access

https://doi.org/10.3390/math9212730

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Abstract

In this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to truth, falsity, reference parameters, and their uncertain linguistic terms to handle problematic and challenging data in factual life impasses. By using the elaborated CLDULSs, some operational laws are also settled. Furthermore, by using the power Einstein (PE) aggregation operators based on CLDULS: the complex linear Diophantine uncertain linguistic PE averaging (CLDULPEA), complex linear Diophantine uncertain linguistic PE weighted averaging (CLDULPEWA), complex linear Diophantine uncertain linguistic PE Geometric (CLDULPEG), and complex linear Diophantine uncertain linguistic PE weighted geometric (CLDULPEWG) operators, and their useful results are elaborated with the help of some remarkable cases. Additionally, by utilizing the expounded works dependent on CLDULS, I propose a multi-attribute decision-making (MADM) issue. To decide the quality of the expounded works, some mathematical models are outlined. Finally, the incomparability and relative examination of the expounded approaches with the assistance of graphical articulations are evolved.

Highlights

multi-attribute decision-making (MADM) is the basic procedure of the dynamic issues whose point is to distinguish the amazingly productive choice(s) from the arrangement of potential ones
If we choose the information in the form of [s1, s2], 0.5ei2π(0.5), 0.3ei2π(0.3), 0.5ei2π(0.5), 0.4ei2π(0.4), at that point, by utilizing the state of intuitionistic FSs (IFSs), complex IFSs (CIFSs), Pythagorean FSs (PFSs), complex PFSs (CPFSs), q-rung orthopair FSs (QROFSs), CQROFSs, linear Diophantine fuzzy set (LDFS), and CLDFS have been fizzled, for adapting to such kinds of issues, the hypothesis of complex linear Diophantine uncertain linguistic set (CLDULS) is an extremely capable and solid method to determine it
CLDULS covers the grade of truth, deception, reference boundaries, and their uncertain etymological terms to achieve with off-kilter and complicated information in genuine life dilemmas

Summary

Introduction

MADM is the basic procedure of the dynamic issues whose point is to distinguish the amazingly productive choice(s) from the arrangement of potential ones. The ideas of IFSs, CIFSs, PFSs, CPFSs, QROFSs, CQROFSs, LDFSs, LDULS, and CLDFSs have various applications in different fields; these hypotheses have their limitations, identified with the enrollment and non-participation grades To annihilate these restrictions, we present the original idea of CLDULS with the expansion of reference boundaries and dubious semantic terms. If we choose the information in the form of [s1, s2], 0.5ei2π(0.5), 0.3ei2π(0.3) , 0.5ei2π(0.5), 0.4ei2π(0.4) , at that point, by utilizing the state of IFSs, CIFSs, PFSs, CPFSs, QROFSs, CQROFSs, LDFSs, and CLDFS have been fizzled, for adapting to such kinds of issues, the hypothesis of CLDULS is an extremely capable and solid method to determine it. To discover the incomparability and consistency of the explained administrators with the assistance of similar investigation and their graphical articulations The objective of this composition is following as: In Section 2, we momentarily appraisal some overall ideas like CFSs, LDFSs, ULSs, and their functional laws. Β ∈ [0, 1], the Einstein T-norm and T-conorm are initiated by: α

Complex Linear Diophantine Uncertain Linguistic Sets

BC 1 BC

AC 11 AACC 1 ACAC

MADM Technique Based on Elaborated Operators

Methods

Conclusions